Number Theory

Por • 15 ago, 2021 • Sección: Ambiente

Number theory is a vast and fascinating field of mathematics, sometimes called «higher arithmetic,» consisting of the study of the properties of whole numbers. Primes and prime factorization are especially important in number theory, as are a number of functions such as the divisor functionRiemann zeta function, and totient function. Excellent introductions to number theory may be found in Ore (1988) and Beiler (1966). The classic history on the subject (now slightly dated) is that of Dickson (2005abc).

The great difficulty in proving relatively simple results in number theory prompted no less an authority than Gauss to remark that «it is just this which gives the higher arithmetic that magical charm which has made it the favorite science of the greatest mathematicians, not to mention its inexhaustible wealth, wherein it so greatly surpasses other parts of mathematics.» Gauss, often known as the «prince of mathematics,» called mathematics the «queen of the sciences» and considered number theory the «queen of mathematics» (Beiler 1966, Goldman 1997).

SEE ALSO:Abstract AlgebraAdditive Number TheoryAlgebraic Number TheoryAnalytic Number TheoryArithmeticComputational Number TheoryCongruenceDiophantine EquationDivisor FunctionElementary Number TheoryGödel’s First Incompleteness TheoremGödel’s Second Incompleteness TheoremMultiplicative Number TheoryNumber Theoretic FunctionPeano’s AxiomsPrime Counting FunctionPrime FactorizationPrime NumberQuadratic Reciprocity TheoremRiemann Zeta FunctionTotient Function

REFERENCES:

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Beiler, A. H. Recreations in the Theory of Numbers: The Queen of Mathematics Entertains, 2nd ed. New York: Dover, 1966.

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Dickson, L. E. History of the Theory of Numbers, Vol. 1: Divisibility and Primality. New York: Dover, 2005a.

Dickson, L. E. History of the Theory of Numbers, Vol. 2: Diophantine Analysis. New York: Dover, 2005b.

Dickson, L. E. History of the Theory of Numbers, Vol. 3: Quadratic and Higher Forms. New York: Dover, 2005c.

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Goldman, J. R. The Queen of Mathematics: An Historically Motivated Guide to Number Theory. Wellesley, MA: A K Peters, 1997.

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Lenstra, H. W. and Tijdeman, R. (Eds.). Computational Methods in Number Theory, 2 vols. Amsterdam: Mathematisch Centrum, 1982.

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Referenced on Wolfram|Alpha: Number Theory

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Weisstein, Eric W. «Number Theory.» From MathWorld–A Wolfram Web Resource. https://mathworld.wolfram.com/NumberTheory.html

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